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As you state the F number is just the ratio of the focal length and the diameter.
For visual use the f number is not very important. The overall light collecting ability (Diameter) determines the brightness of the image. Stars are point sources of light. The magnification you see of extended sources is determined by what eyepiece you use.
For photography the F number determines the field of view. For a constant diameter scope the one with the lower f number will have a larger field of view. This will concentrate extended sources (ie nebulas and galaxies) into a smaller area making them appear brighter on the image. The trade off is that they are smaller but for big objects this is good. For little galaxies or nebulas it isn't as good.
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